The document discusses the properties of integers. Integers include positive and negative whole numbers along with zero. Integers have closure properties under addition and subtraction. They also have commutative and associative properties for addition. Zero is the additive identity for integers. Integers are closed under multiplication and one is the multiplicative identity. Division of integers has closure and communality properties when the divisor is not equal to zero.

1. INTEGER
V.SARANYA 7TH B
22
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2. Introduction
 The whole numbers and negative numbers
together form integers.
 Integers are the collection of positive and
negative numbers along with ‘0’ .



3. Contents :
Closure property
Commutative property
Associative property
Additive identity

4. Closure property
 Addition : for any 2 integers a and b , a+b is
also a an integer .ex : (-5)+3=(-2)
 Therefore we say that integers are closed
under addition .
 Subtraction : for any 2 integers a and b , a-b is
also an integer .ex : (-5) – (-3) = (-8)
 Therefore we say that integers are closed
under subtraction .

5. Commutative property
 For any integer a and b , a+b = b+a . Ex : 3+(-
2)=1 = (-2)+3=1
 Therefore we say that addition is commutative
for integers .
 Subtraction is not commutative for integers .

6. Associative property and additive
identity
 Associative identity:
 For any integers a ,b ,c , a+(b+c) = (a+b) +c
 Therefore we say that addition is associative
for integers .
 Subtraction is not associative for integers.
 For any integers a , a+0=a .
 Therefore we say that ‘0’ is the additive
identity for integers

7. Contents :
Closure property
Commutative property
Multiplication by ‘0’
Multiplicative identity
Associative property
Distributive property

8. Closure property
 For any integers a and b, a*b is also an integer
.
 Ex : (-50)*3=(-15)
 For any integers a and b , a*b=b*a
 Ex : (-2)*3 = 3*(-2)
 Any integer multiplied by zero , is zero itself .

9. Multiplicative identity
 For any integer a , a*1 = 1*a = a .
 Ex : (-4)*1=(-4)
 For any integers a , b and c , (a*b)*c = a*(b*c)
.
 Ex : [ (-4)*6 ]* (-5) = 4*[ 6*(-5) ]
 For any integer a , b and c , a*b+c=a*b=b*c
 Ex :- 16*[10+2] = [16*10]+[16+2]

10. Division of integers
For any integers a and b , a/[-b] =
[-a]/b ( where b is not equal to 0
Properties of division of integer
Closure property
Communality

11. Closure property
 Division is closed for any integer
 Ex :- [ 1 ] [ -25 ] / 5 = [ -5 ]
[ 2 ] 15 / [ -3 ] = [ -5 ]
Division is not closed under integers
For any integer a , a / 1 = a
Ex : - [ -12 ] / 1 = [ -12 ]
[ -4 ] / 1 = [ -4 ]